(7x+1)/(6x)=(4x+2)/(6x-4)

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Solution for (7x+1)/(6x)=(4x+2)/(6x-4) equation:


D( x )

6*x = 0

6*x-4 = 0

6*x = 0

6*x = 0

6*x = 0 // : 6

x = 0

6*x-4 = 0

6*x-4 = 0

6*x-4 = 0 // + 4

6*x = 4 // : 6

x = 4/6

x = 2/3

x in (-oo:0) U (0:2/3) U (2/3:+oo)

(7*x+1)/(6*x) = (4*x+2)/(6*x-4) // - (4*x+2)/(6*x-4)

(7*x+1)/(6*x)-((4*x+2)/(6*x-4)) = 0

(7*x+1)/(6*x)+(-1*(4*x+2))/(6*x-4) = 0

((7*x+1)*(6*x-4))/(6*x*(6*x-4))+(-1*6*x*(4*x+2))/(6*x*(6*x-4)) = 0

(7*x+1)*(6*x-4)-1*6*x*(4*x+2) = 0

18*x^2-34*x-4 = 0

18*x^2-34*x-4 = 0

2*(9*x^2-17*x-2) = 0

9*x^2-17*x-2 = 0

DELTA = (-17)^2-(-2*4*9)

DELTA = 361

DELTA > 0

x = (361^(1/2)+17)/(2*9) or x = (17-361^(1/2))/(2*9)

x = 2 or x = -1/9

2*(x+1/9)*(x-2) = 0

(2*(x+1/9)*(x-2))/(6*x*(6*x-4)) = 0

(2*(x+1/9)*(x-2))/(6*x*(6*x-4)) = 0 // * 6*x*(6*x-4)

2*(x+1/9)*(x-2) = 0

( x+1/9 )

x+1/9 = 0 // - 1/9

x = -1/9

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -1/9, 2 }

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